import numpy as np
from typing import Tuple
import autoarray as aa
from autogalaxy.cosmology.lensing import LensingCosmology
from autogalaxy.cosmology.wrap import Planck15
from autogalaxy.profiles.mass.dark.abstract import AbstractgNFW
[docs]class NFWTruncatedSph(AbstractgNFW):
def __init__(
self,
centre: Tuple[float, float] = (0.0, 0.0),
kappa_s: float = 0.05,
scale_radius: float = 1.0,
truncation_radius: float = 2.0,
):
super().__init__(
centre=centre,
ell_comps=(0.0, 0.0),
kappa_s=kappa_s,
inner_slope=1.0,
scale_radius=scale_radius,
)
self.truncation_radius = truncation_radius
self.tau = self.truncation_radius / self.scale_radius
[docs] @aa.grid_dec.grid_2d_to_vector_yx
@aa.grid_dec.grid_2d_to_structure
@aa.grid_dec.transform
@aa.grid_dec.relocate_to_radial_minimum
def deflections_yx_2d_from(self, grid: aa.type.Grid2DLike, **kwargs):
"""
Calculate the deflection angles at a given set of arc-second gridded coordinates.
Parameters
----------
grid
The grid of (y,x) arc-second coordinates the deflection angles are computed on.
"""
eta = np.multiply(1.0 / self.scale_radius, self.radial_grid_from(grid=grid))
deflection_grid = np.multiply(
(4.0 * self.kappa_s * self.scale_radius / eta),
self.deflection_func_sph(grid_radius=eta),
)
return self._cartesian_grid_via_radial_from(grid, deflection_grid)
def deflection_func_sph(self, grid_radius):
grid_radius = grid_radius + 0j
return np.real(self.coord_func_m(grid_radius=grid_radius))
def convergence_func(self, grid_radius: float) -> float:
grid_radius = ((1.0 / self.scale_radius) * grid_radius) + 0j
return np.real(2.0 * self.kappa_s * self.coord_func_l(grid_radius=grid_radius))
@aa.grid_dec.grid_2d_to_structure
def potential_2d_from(self, grid: aa.type.Grid2DLike):
return np.zeros(shape=grid.shape[0])
def coord_func_k(self, grid_radius):
return np.log(
np.divide(
grid_radius,
np.sqrt(np.square(grid_radius) + np.square(self.tau)) + self.tau,
)
)
def coord_func_l(self, grid_radius):
f_r = self.coord_func_f(grid_radius=grid_radius)
g_r = self.coord_func_g(grid_radius=grid_radius)
k_r = self.coord_func_k(grid_radius=grid_radius)
return np.divide(self.tau**2.0, (self.tau**2.0 + 1.0) ** 2.0) * (
((self.tau**2.0 + 1.0) * g_r)
+ (2 * f_r)
- (np.pi / (np.sqrt(self.tau**2.0 + grid_radius**2.0)))
+ (
(
(self.tau**2.0 - 1.0)
/ (self.tau * (np.sqrt(self.tau**2.0 + grid_radius**2.0)))
)
* k_r
)
)
def coord_func_m(self, grid_radius):
f_r = self.coord_func_f(grid_radius=grid_radius)
k_r = self.coord_func_k(grid_radius=grid_radius)
return (self.tau**2.0 / (self.tau**2.0 + 1.0) ** 2.0) * (
((self.tau**2.0 + 2.0 * grid_radius**2.0 - 1.0) * f_r)
+ (np.pi * self.tau)
+ ((self.tau**2.0 - 1.0) * np.log(self.tau))
+ (
np.sqrt(grid_radius**2.0 + self.tau**2.0)
* (((self.tau**2.0 - 1.0) / self.tau) * k_r - np.pi)
)
)
def mass_at_truncation_radius_solar_mass(
self,
redshift_profile,
redshift_source,
redshift_of_cosmic_average_density="profile",
cosmology: LensingCosmology = Planck15(),
):
mass_at_200 = self.mass_at_200_solar_masses(
redshift_object=redshift_profile,
redshift_source=redshift_source,
redshift_of_cosmic_average_density=redshift_of_cosmic_average_density,
cosmology=cosmology,
)
return (
mass_at_200
* (self.tau**2.0 / (self.tau**2.0 + 1.0) ** 2.0)
* (
((self.tau**2.0 - 1) * np.log(self.tau))
+ (self.tau * np.pi)
- (self.tau**2.0 + 1)
)
)